There are a couple reasons (depending on interpretation) why she would drink.

1. The King has proposed drinking on Hamlet's touches in the fencing bout. The Queen, proud of her son, is involved in the match because Hamlet scores two hits in a row and drinks to his success (she "carouses" to his fortune).

2. She has a suspicion which is confirmed by the panic in Claudius' line "Gertrude, do not drink." She would figure out that there's poison in the cup and drink it anyway. She's discovered his treachery and doesn't want to be a part of it.

Even if she suspects there's poison, it could be interpreted as a kind of Russian Roulette. She's thinking, "If I drink this and there's no poison, it's OK. If there actually is poison, it confirms the treachery and I don't want to live."

You wrote “a couple of reasons”. However, my question is “why does Gertrud take up a drink?”, to be precise. So, your answers would be the steps to the death or, in that point of view, “suicide” of Gertrud. So the numbered 1 is the answer for my question, I think.

By the way, I am a native Japanese. Writing my thoughts in English is so hard for me. As a result, there could be many strange or rude expressions, I’m afraid. But, believe me, there’s no intentions to be impolite. I’d like to wholeheartedly say thanks to your reply to my question.

Anyway, back to the original story….

My biggest concern is here. How and where does the answer by Gertrud appear?

In the Scene 11, Hamlet gives her a delicate proposition, when she tries to give him “good night blessing” as his mother, I think, just like Polonius gives some blessings to his son Laertes, as his father, in the Scene 3. By which, in some ways I think, Shakespeare wanted to present “normal family” with no bad secret among them.

But, in the Scene 11 Hamlet refuses to be blessed by his mother Gertrud. And say …

"once more good night,
And when you are desirous to be blest,
Ile blessing beg of you," (Q2)

That means he declares that he will stop or hold the Mother and son relationship between Gertrud and himself, until she truly repents her sin. I think this is the biggest problem for her.

Then, please remember the Ghost’s words in the Scene 5.

leaue her to heauen,
And to those thornes that in her bosome lodge
To prick and sting her,

After the Scene 11, all the Gertrud scenes hold this theme. Gertrud begins to repent her sin.

So, “How and where does the answer by Gertrud appear?”.

It is prolonged to the last scene. And finally she declares “The Queene carowses to thy fortune Hamlet.”

Blessing, I think.

Then, Hamlet responds with “Good Madam”, not a word of thanks. "Good Madam."

At the moment, although Claudius says “Gertrude, do not drinke.” but she drinks with these words,

You wrote “a couple of reasons”. However, my question is “why does Gertrud take up a drink?”, to be precise. So, your answers would be the steps to the death or, in that point of view, “suicide” of Gertrud. So the numbered 1 is the answer for my question, I think.

Both work, but choose the one that works best for you. Kouichi Yoshii wrote:

By the way, I am a native Japanese. Writing my thoughts in English is so hard for me. As a result, there could be many strange or rude expressions, I’m afraid. But, believe me, there’s no intentions to be impolite. I’d like to wholeheartedly say thanks to your reply to my question.

No problem.Kouichi Yoshii wrote:

My biggest concern is here. How and where does the answer by Gertrud appear?

I'm not sure I understand this question. What "answer"?Kouichi Yoshii wrote:

In the Scene 11, Hamlet gives her a delicate proposition, when she tries to give him “good night blessing” as his mother, I think, just like Polonius gives some blessings to his son Laertes, as his father, in the Scene 3. By which, in some ways I think, Shakespeare wanted to present “normal family” with no bad secret among them.

But, in the Scene 11 Hamlet refuses to be blessed by his mother Gertrud. And say …

"once more good night,
And when you are desirous to be blest,
Ile blessing beg of you," (Q2)

That means he declares that he will stop or hold the Mother and son relationship between Gertrud and himself, until she truly repents her sin. I think this is the biggest problem for her.

Are you trying to draw a connection between this passage and Gertrude drinking the poison? If so, I don't see the connection.Kouichi Yoshii wrote:

Then, please remember the Ghost’s words in the Scene 5.

leaue her to heauen,
And to those thornes that in her bosome lodge
To prick and sting her,

After the Scene 11, all the Gertrud scenes hold this theme. Gertrud begins to repent her sin.

What sin is she repenting here? Well, let me ask you this.... what do you think the "thorns" are?Kouichi Yoshii wrote:

So, “How and where does the answer by Gertrud appear?”.

It is prolonged to the last scene. And finally she declares “The Queene carowses to thy fortune Hamlet.”

Blessing, I think.

Then, Hamlet responds with “Good Madam”, not a word of thanks. "Good Madam."

At the moment, although Claudius says “Gertrude, do not drinke.” but she drinks with these words,

“I will my Lord, I pray you pardon me”.

However, unfortunately, the cup is poisoned.

Maybe you can explain what you are trying to accomplish and I can see if I (or someone else) can help.

Thanks. Yes, both work, in a sense. For example, Gertrude in David Tennant’s Hamlet. The final scene explains the motivation of Gertrude’s suicide very well. However, from the perspective of this whole drama, question remains. No one in this drama knows her thoughts at all, except for the audience and, of course, the author. So, Horatio who will have to become a story teller of this tragedy can not refer to her suicide in his “summary speech” for Fortenbrasse. I’'d say it is too novelistic, not “dramatic”. Of course, again, in a sense.

I have to echo Ron in relationship to interpreting the last scene and whether this is suicide or accidental murder of Gertrude. From an interpretation point of view both work. As a director/performer my instinct is that the 'accidental murder' interpretation works without any additional support from other scenes. If you chose to perform with the 'suicide' interpretation, then I believe you would need to review character development in preceeding scenes for either of two aspects - that Gertrud's ongoing guilt drives her to seek an end via death OR that she quickly relises, from that one statement of 'do not drink' from Claudius that the fight is rigged and Hamlet will die, and so takes his poison instead, as a sacrifice to keep him alive. My viewing of the Tennant film is the later interpretation - but this is just a personal assessment.

Being performed, I would be worried that the 'suicide' interpretations may be overworking the script and compromise the impact of this last scene for the majority of the audience, but may hold some appeal to those who study Shakespeare.